A circuit has four inputs D, C, B, A encoded in 8421 natural binary form.

The inputs in

the range 0000

2

= 0 to 1011

2

= 11 represent the months of the

year from January (0) to December (11). The output

of the circuit is a logical

true

if the month represented by the input has 31 days. Otherwise the output

is false.

Inputs in the range 1100 to

1111 (i.e., 12 to 15) cannot occur

(dont

care

on K

-

map

)

.

a)

Draw a truth table to represent the problem and use it to construct a

Karnaugh map.

b)

Use the Karnaugh map to obtain a simplified expression for the

function.

c)

Construct a circuit to implement the

function using AND, OR and

NOT gates.

d)

Construct a circuit to implement the function using NAND gates only.